Once the police are involved it is up to the prosecutors office to charge you with a crime. Your friend at this point does not have the option of "dropping charges".
From what you've posted above it sounds like this is a simple misdemeanor battery (Ca Penal Code Section 242) unless there was some type of dating or sexual relationship with this woman, then it would be considered a domestic violence charge which can either be a misdemeanor or a battery, depending on whether there were any injuries. A misdemeanor battery is 6 months max in jail, and a domestic violence charge can either be 1 year in jail, or if a felony, the sentencing range is 16 months as the low tern, 2 years as the mid term, and 3 years as the max in state prison.
Make sure to keep an eye on your mail - the prosecutors may send you a letter in the mail indicating they have filed a case against you. The best thing to do is take care of it right away and talk to a good lawyer.
You should be consulting with locally experienced attorneys who will be able to assist you on a "pre-file/investigatory" basis. Do not make any further statements to law enforcement and/or this woman without counsel present.
David P. Shapiro
This sounds like an overblown situation, but there is always the possibility of filing of criminal charges - from what you describe (from your memory although you were drinking), it sounds like misdemeanor conduct at best.
Given all that you wrote, you may want to consult with a criminal defense attorney to run some interference for you to try and avoid the filing of charges. Mr. Shapiro would be an excellent place to start.